Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

p?gbtrf

Computes the
LU
 factorization of a general n-by-n banded distributed matrix.

Syntax

void
psgbtrf
(
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
float
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
float
*af
,
MKL_INT
*laf
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdgbtrf
(
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
double
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
double
*af
,
MKL_INT
*laf
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pcgbtrf
(
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_Complex8
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex8
*af
,
MKL_INT
*laf
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pzgbtrf
(
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_Complex16
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex16
*af
,
MKL_INT
*laf
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
Include Files
  • mkl_scalapack.h
Description
The
p?gbtrf
function
computes the
LU
 factorization of a general
n
-by-
n
 real/complex banded distributed matrix
A
(1:
n
,
ja
:
ja
+
n
-1) using partial pivoting with row interchanges.
The resulting factorization is not the same factorization as returned from the LAPACK
function
?gbtrf
. Additional permutations are performed on the matrix for the sake of parallelism.
The factorization has the form
A
(1:
n
,
ja
:
ja
+
n
-1) =
P
*
L
*
U
*
Q
where
P
 and
Q
 are permutation matrices, and
L
 and
U
 are banded lower and upper triangular matrices, respectively. The matrix
Q
 represents reordering of columns for the sake of parallelism, while
P
 represents reordering of rows for numerical stability using classic partial pivoting.
Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.
Notice revision #20201201
Input Parameters
n
(global) The number of rows and columns in the distributed submatrix
A
(1:
n
,
ja
:
ja
+
n
-1);
n
≥
 0
.
bwl
(global) The number of sub-diagonals within the band of
A
( 0 ≤
bwl
 ≤
n-1
 )
.
bwu
(global) The number of super-diagonals within the band of
A
( 0 ≤
bwu
 ≤
n-1
 )
.
a
(local)
Pointer into the local memory to an array of local size
lld_a
*
LOCc
(
ja
+
n
-1)
 where
lld_a
≥
 2*
bwl
 + 2*
bwu +1
.
Contains the local pieces of the
n
-by-
n
 distributed banded matrix
A
(1:
n
,
ja
:
ja
+
n
-1) to be factored.
ja
(global) The index in the global matrix
A
 indicating the start of the matrix to be operated on (which may be either all of
A
 or a submatrix of
A
).
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
If
dtype_a
 = 501
, then
dlen_
≥
 7
;
else if
dtype_a
 = 1
, then
dlen_
≥
 9
.
laf
(local) The size of the array
af
.
Must be
laf
≥
 (
nb_a
+
bwu
)*(
bwl
+
bwu
)+6*(
bwl
+
bwu
)*(
bwl
+2
*bwu
)
.
If
laf
 is not large enough, an error code will be returned and the minimum acceptable size will be returned in
af
[0]
.
work
(local) Same type as
a
. Workspace array of size
lwork
.
lwork
(local or global) The size of the
work
 array
(
lwork
≥
 1)
. If
lwork
 is too small, the minimal acceptable size will be returned in
work
[0]
 and an error code is returned.
Output Parameters
a
On exit, this array contains details of the factorization. Note that additional permutations are performed on the matrix, so that the factors returned are different from those returned by
LAPACK
.
ipiv
(local) array.
The size of
ipiv
 must be
≥
nb_a
.
Contains pivot indices for local factorizations. Note that you
should not alter
 the contents of this array between factorization and solve.
af
(local)
Array of size
laf
.
Auxiliary fill-in space. The fill-in space is created in a call to the factorization
function
p?gbtrf
 and is stored in
af
.
Note that if a linear system is to be solved using
p?gbtrs
 after the factorization
function
,
af
 must not be altered after the factorization.
work
[0]
On exit,
work
[0]
 contains the minimum value of
lwork
 required.
info
(global)
If
info
=0
, the execution is successful.
info
 < 0
:
If the
i
-th argument is an array and the
j-
th entry
, indexed
j
 - 1,
 had an illegal value, then
info
 = -(
i
*100+
j
); if the
i-
th argument is a scalar and had an illegal value, then
info
 =
-i
.
info
>
 0
:
If
info
 =
k
 ≤
NPROCS
, the submatrix stored on processor
info
 and factored locally was not nonsingular, and the factorization was not completed.
If
info
 =
k
 >
NPROCS
, the submatrix stored on processor
info
-
NPROCS
 representing interactions with other processors was not nonsingular, and the factorization was not completed.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.